SPURIOUS CORRELATION AND IT'S DETECTION
Although statisticians warn against the flaw of spurious
correlation, little or nothing is suggested as to how to
identify its presence other than to critically examine the
conclusions. In cross-sectional analysis, the phenomena of
spurious correlation can be observed by injecting structure
by creating ratios with a common denominator.
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Early authors like Bartlett (1931) asked "Why do we
sometimes get spurious correlation between time series". The
presence of ARIMA structure usually reflects omitted input
series or incorrect lag structures. Time series analysts who
correctly augment their model with ARIMA structure
can and do expose the spurious nature of a candidate input.
This is demonstrated in the Australian Wine Study. Spurious
correlation induced by omitted Intervention series is exposed in
the Demand For Gas Study.
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The concept of incorporating needed but omitted variables
is clear in time series because the concomitant variable is
usually obvious after its presence has been detected via
ARIMA structure with a conclusion that the X variable is not
significant above and beyond the historical impact of Y.
There are many cases where the ARIMA structure , having reduced
the error variance enables a clearer picture and the significance
of a candidate variable. The Income/Consumption study illustrates
this rather nicely.
This process of identification usually arises when
conclusions are drawn like "fireman cause damage" or "storks
bring babies" or "the number of words in a person's
vocabulary depends on their foot size" or "beer is
a snob good because actual price was used rather than real price.".
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